RELATED RATE WORD PROBLEMS

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Poppy Martin
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1 Mat RELATED RATE WORD PROBLEMS Sock. A stone town into a pon pouces a cicula ipple tat epans fom te point of impact. If te aius of te ipple inceases at a ate of.5 ft/sec ow fast is te aea gowing wen te aius is 8 feet?. If te lengt of a sie of a cube in inceasing at a ate of 5 in/sec ow fast is te volume inceasing wen te lengt of a sie is in?. A bo is fling a kite at a eigt of 50 ft. If te kite moves oizontall awa fom te bo at te ate of 0 ft/sec ow fast is te sting being pai out wen te kite is 50 ft fom te bo?. A 6 foot man walks awa fom a foot lamp post at te ate of ft/sec. How fast is is saow lengtening wen e is feet fom te post? 5. Two cas leave an intesection. One tavels not at 0mp te ote tavels east at 0mp. How fast is te istance between tem inceasing at te en of 0 minutes? 6. A speical balloon is inflate at a ate of ft /min. How fast is te aius inceasing wen te aius is ft? 7. You ae blowing a bubble wit bubble gum an can blow ai into te bubble at a ate of in / sec. At wat ate is te aius inceasing wen te aius is inces? 8. A speical snowball is place in te sun. Te sun melts te snowball so tat its aius eceases 0.5 in/. Fin te ate of cange in volume w..t time at te instant te aius is inces. 9. A lage speical balloon is inflate b a pump tat injects 0 ft /sec of elium. At te instance wen te balloon contains 97π ft of gas ow fast is its aius canging? 0. Gas is escaping fom a speical balloon at a ate of ft /min. How fast is te suface aea sinking wen te aius is ft?. If te volume of an epaning cube is inceasing at te ate of ft /min ow fast is its suface aea inceasing wen te suface is ft?. A 0 foot lae leans against a vetical builing. If te bottom of te lae slies awa fom te builing oizontall at a ate of ft/sec ow fast is te lae sliing own te builing wen te top of te lae is feet above te goun?. A 5 foot lae leans against a vetical wall. If te top slies ownwa at te ate of ft/sec fin te spee of te lowe en wen it is feet fom te wall.. A two-piece etension lae leaning against a wall is collapsing at a ate of ft/sec. wile te foot of te lae emains a constant 5 ft fom te wall. How fast is te lae moving own te wall wen te lae is ft. long? 5. A balloon is ising veticall at a ate of ft/sec. An obseve is locate 00 ft fom a point on te goun iectl below te balloon. At wat ate is te istance between te balloon an te obseve canging wen te eigt of te balloon is 00 ft? 6. A conical tank as aius ft an ept 0 ft. If wate is poue into te tank at te ate of ft /min ow fast is te wate level ising wen te wate in te tank is 5 ft eep? 7. Wate flows into an invete conical tank at te ate of 7 ft / min. Wen te ept of te wate is ft ow fast is te level ising? Assume te eigt of te tank is ft an te aius at te top is ft. 8. San is pouing fom a pipe at te ate of ft /sec. If te falling san foms a conical pile on te goun wose eigt is alwas / te iamete of te base ow fast is te eigt inceasing wen te pile is ft ig? 9. A baseball plae uns fom ome plate to fist base at a ate of 5 ft/sec. At wat ate is is istance fom ti base canging wen e is 0 ft fom fist base? A baseball iamon is a 90 ft b 90 ft squae. 0. Te top of a towe as te sape of te emispee of aius 5 ft. Te top as a unifom coating of ice wic is inces tick. Te tickness of te ice is eceasing at te ate of / in pe ou. How fast is te volume of te ice canging?. A toug 0 ft long as a coss section tat is an isosceles tiangle aving a base of ft an eigt ft. If wate pous into te toug at a ate of 6 ft /min ow fast is te ept of te wate canging wen te ept is ft?. A beacon 0.5 miles (pepenicula istance) fom a staigt soe evolves at evolutions pe minute (π aians pe minute). At wat spee is te beam moving along te soe wen it its te soe mile fom te ligtouse?

2 Mat Sock. A stone town into a pon pouces a cicula ipple tat epans fom te point of impact. If te aius of te ipple inceases at a ate of.5 ft/sec ow fast is te aea gowing wen te aius is 8 feet? A A π ft / sec? wen 8 ft A A A A π π (8) π ft /sec. If te lengt of a sie of a cube in inceasing at a ate of 5 in/sec ow fast is te volume inceasing wen te lengt of a sie is in? 5 in / sec? wen in () 5 60 in /sec. A bo is fling a kite at a eigt of 50 ft. If te kite moves oizontall awa fom te bo at te ate of 0 ft/sec ow fast is te sting being pai out wen te kite is 50 ft fom te bo?? ft / sec wen 50 ft ft /sec. A 6 foot man walks awa fom a foot lamp post at te ate of ft/sec. How fast is is saow lengtening wen e is feet fom te post? 6 a b a 6 a b b an a + b b a b ft /sec b a + b

3 Mat Sock 5. Two cas leave an intesection. One tavels not at 0mp te ote tavels east at 0mp. How fast is te istance between tem inceasing at te en of 0 minutes? (0)(0) + (5)(0) 50 mp 6. A speical balloon is inflate at a ate of ft /min. How fast is te aius inceasing wen te aius is ft? π π? wen π () ft / min π 7. You ae blowing a bubble wit bubble gum an can blow ai into te bubble at a ate of in / sec. At wat ate is te aius inceasing wen te aius is inces? π π? wen π () in /sec π 8. A speical snowball is place in te sun. Te sun melts te snowball so tat its aius eceases 0.5 in/. Fin te ate of cange in volume w..t time at te instant te aius is inces. π π? wen π () 6π in /

4 Mat Sock 9. A lage speical balloon is inflate b a pump tat injects 0 ft /sec of elium. At te instance wen te balloon contains 97π ft of gas ow fast is its aius canging? π 0 97π π 9 π? wen 97π 0 π (9) 0 ft /sec π 0. Gas is escaping fom a speical balloon at a ate of ft /min. How fast is te suface aea sinking wen te aius is ft? π π S? wen π () ft / min 88π S π s S 8π 8π () 88π ft / min. If te volume of an epaning cube is inceasing at te ate of ft /min ow fast is its suface aea inceasing wen te suface is ft? S 6 6 s? wen S () S () 8 ft / min. A 0 foot lae leans against a vetical builing. If te bottom of te lae slies awa fom te builing oizontall at a ate of ft/sec ow fast is te lae sliing own te builing wen te top of te lae is feet above te goun? ? wen 0 0 (6)() ( ) 8 ft /sec

5 Mat Sock. A 5 foot lae leans against a vetical wall. If te top slies ownwa at te ate of ft/sec fin te spee of te lowe en wen it is feet fom te wall ? wen () (9)() ft /sec. A two-piece etension lae leaning against a wall is collapsing at a ate of ft/sec. wile te foot of te lae emains a constant 5 ft fom te wall. How fast is te lae moving own te wall wen te lae is ft. long? L 5 5 L 5 L? wen L 5 L L L () ()( ) ft / sec 6

6 Mat Sock 5. A balloon is ising veticall at a ate of ft/sec. An obseve is locate 00 ft fom a point on te goun iectl below te balloon. At wat ate is te istance between te balloon an te obseve canging wen te eigt of te balloon is 00 ft? ? wen (00)() (500) 8 ft /sec 5 6. A conical tank as aius ft an ept 0 ft. If wate is poue into te tank at te ate of ft /min ow fast is te wate level ising wen te wate in te tank is 5 ft eep? 0 0? wen 5 0 π 9π 00 π 0 9π (5) 00 8 ft / min 9π π 00

7 Mat Sock 7. Wate flows into an invete conical tank at te ate of 7 ft / min. Wen te ept of te wate is ft ow fast is te level ising? Assume te eigt of te tank is ft an te aius at te top is ft. 7? wen π π 8 π π () ft / min π π 8 8. San is pouing fom a pipe at te ate of ft /sec. If te falling san foms a conical pile on te goun wose eigt is alwas / te iamete of te base ow fast is te eigt inceasing wen te pile is ft ig? () wen 6.? wen π 9π π 9π () ft /sec π π

8 Mat Sock 9. A baseball plae uns fom ome plate to fist base at a ate of 5 ft/sec. At wat ate is is istance fom ti base canging wen e is 0 ft fom fist base? A baseball iamon is a 90 ft b 90 ft squae. n 90 P H st (50)(5) ft /sec 06 5 Fin wen Te top of a towe as te sape of te emispee of aius 5 ft. Te top as a unifom coating of ice wic is inces tick. Te tickness of te ice is eceasing at te ate of / in pe ou. How fast is te volume of te ice canging? 5 ft 60 in π π π π ( 60 + ) π ( 60) ( 60 + ) π ( 60) ( 60 + ) ( 60 + ) 66π in Fin / wen.

9 Mat Sock. A toug 0 ft long as a coss section tat is an isosceles tiangle aving a base of ft an eigt ft. If wate pous into te toug at a ate of 6 ft /min ow fast is te ept of te wate canging wen te ept is ft? 0 0.5w 0.5w w w 6 Fin b 0 w 0 5w ( ) 5 0 wen ft / min. A beacon 0.5 miles (pepenicula istance) fom a staigt soe evolves at evolutions pe minute (π aians pe minute). At wat spee is te beam moving along te soe wen it its te soe mile fom te ligtouse? ½ mi θ / θ sec θ cosθ θ π tanθ sec θ Fin wen tanθ θ. θ θ sec θ π ( ) π 8π mi / min

How can you compare lengths between the customary and metric systems? 6 ft. ACTIVITY: Customary Measure History

How can you compare lengths between the customary and metric systems? 6 ft. ACTIVITY: Customary Measure History 5.7 Converting Measures How can you compare lengts between te customary and metric systems? yd 6 ft ACTIVITY: Customary Measure History COMMON CORE Converting Measures In tis lesson, you will use conversion